A posteriori error estimation for a C¹ virtual element method of Kirchhoff plates

A residual-type a posteriori error estimation is developed for a C-1-conforming virtual element method (VEM) to solve a Kirchhoff plate bending problem. To derive the reliability and efficiency of the a posteriori error bound, the inverse inequalities and norm equivalence are developed over the underlying C-1-conforming virtual element space, and a weak interpolation operator together with its error estimates is given as well. As an outcome of the error estimator, an adaptive VEM is introduced by means of the mesh refinement strategy with the one-hanging-node rule. Numerical results on various benchmark tests confirm the robustness of the proposed error estimator and show the efficiency of the resulting adaptive VEM.